Question: Simplify the following expression: $r = \dfrac{-30t - 50}{-25t + 55}$ You can assume $t \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-30t - 50 = - (2\cdot3\cdot5 \cdot t) - (2\cdot5\cdot5)$ The denominator can be factored: $-25t + 55 = - (5\cdot5 \cdot t) + (5\cdot11)$ The greatest common factor of all the terms is $5$ Factoring out $5$ gives us: $r = \dfrac{(5)(-6t - 10)}{(5)(-5t + 11)}$ Dividing both the numerator and denominator by $5$ gives: $r = \dfrac{-6t - 10}{-5t + 11}$